Dynamics Study Of A Class Of Lorenz Chaotic Systems With Memristor

Chaos is an inherent characteristic of non-linear systems and exists widely in nature.Its complex dynamic characteristics have attracted the attention of many scholars,and chaos research has become a popular direction in current nonlinear science.As the best component of artificial intelligence,the research of memristor has become hot in recent years with the coming of the era of artificial intelligence.Based on the classical Lorenz system,this paper obtains a class of 3D memristive chaotic system through feedback control,and analyzes the local dynamics of this system.In the first chapter,the origin and development of chaos and memristor are introduced,some theorems and definitions used in this paper are given,and the origin of the system studied in this paper is introduced.In the second chapter,the local linear stability of the system is studied by the linearization method,and the stability conditions at the equilibrium point are obtained.Then,using KCC theory,the Jacobi stability of the system is analyzed,and the Jacobi stability of the system is obtained.These results have some significance to explore the mechanism of chaos.In chapter three,based on the parameter-dependent center manifold theory ?normal form theory and the average theory,we first study the codimension 1 bifurcation like Pitchfork bifurcation and Hopf bifurcation,obtain the stability at non-hyperbolic equilibrium point and the parameter conditions when the system generates periodic solutions.Then we study the codimension 2 bifurcation like Zero-Hopf bifurcation and Double-Zero bifurcation,and find that the results are quite different from the codimension 1 bifurcation,which is helpful to understand the bifurcation behavior of the dynamic system to a certain extent.In chapter four,in order to make up for the shortcomings of local analysis,with the help of Poincaré compactification method,the dynamic behavior of the system at infinity is studied and the state of the singularity at infinity is obtained,to better understand the global dynamic behavior of the system.In the fifth chapter,the simulation software Simulink in MATLAB is used to simulate the theoretical analysis of the previous chapters.It is found that under the given parameter conditions,the simulation results are consistent with the theoretical analysis results,thus confirming the correctness of the analysis in this paper.